[Haskell-beginners] Monads...

[Rafael Gustavo da Cunha Pereira Pinto]

Cory,

The big hit for me was Phillip Wadler's paper "Monads for functional
programming" I made me start thinking "well, this looks like a monad..."

homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baastad.pdf

Cheers

On Thu, Jan 29, 2009 at 01:38, nanothief <nanothief at gmail.com> wrote:

> Cory Knapp wrote:
>
>> Hello, so, I'm having a simple problem with monads: I have no idea how to
>> actually use them. I understand the category theory (or, at least well
>> enough to be able to explain "what is a monad"); I understand the way to
>> declare something as a monad instance, but I just don't get how to program
>> with them. Can anyone provide me with, or direct me towards, some simple
>> monads and some ways of using (for example) the monadic properties of lists?
>>
>> Thanks,
>> Cory
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>>
> I found that http://www.haskell.org/all_about_monads/html/index.html gave
> a lot of nice examples of using list and maybe monads. The list monad is
> particularly useful for finding possible solutions given available input
> values.
> For example, with the problem
> x + 8y = 114
> 3x - 8y + 4z = 182
> x < y < z < 100
> Find solutions for x,y,z
>
> The program:
> res :: [(Int,Int,Int)]
> res = do
>  x <- [1..100]
>  y <- [1..100]
>  z <- [1..100]
>  guard $ x + 8 * y == 114
>  guard $ 3*x - 8*y + 4*z == 182
>  guard $ x < y
>  guard $ y < z
>  return (x,y,z)
>
> will output all the possible solutions. Note how close the program is to
> the actual problem. The values of x,y, and z are chosen from the value
> [1..100], but if a guard statement fails, the (x,y,z) choice is abandoned.
>
> Another example (taken from
> http://www.mathsisfun.com/puzzles/sum-of-digits-is-43-solution.html )
> *The Puzzle:* I am thinking of a 6-digit number. The sum of the digits is
> 43.
>
> And only two of the following three statements about the number are true:
>
> (1) it's a square number,
> (2) it's a cube number, and
> (3) the number is under 500000.
>
> the program
> answer = do
>  d1 <- [0..9]
>  d2 <- [0..9]
>  d3 <- [0..9]
>  d4 <- [0..9]
>  d5 <- [0..9]
>  d6 <- [0..9]
>  let digitSum = d1 + d2 + d3 + d4 + d5 + d6
>  let value = d1 + d2*10 + d3*100 + d4*1000 + d5*10000 + d6*100000
>  guard $ digitSum == 43
>  let lessThan500000 = digitSum < 500000
>  let isSquare = (round $ sqrt (fromIntegral value)) ^ 2 == value
>  let isCube = (round $ (fromIntegral value) ** (1/3)) ^ 3 == value
>  guard $ length (filter id [lessThan500000,isSquare,isCube]) == 2
>  return value
>
> will output the three answers (not that the author only found one
> solution!).
>
>
>
>
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>



-- 
Rafael Gustavo da Cunha Pereira Pinto
Electronic Engineer, MSc.
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